Abstract
We perform an exact computation of the gauged linear sigma model associated to a D1-D5 brane system on a resolved A 1 singularity. This is accomplished via supersymmetric localization on the blown-up two-sphere. We show that in the blow-down limit \( {{{{{\mathbb{C}}^2}}} \left/ {{{{\mathbb{Z}}_2}}} \right.} \) the partition function reduces to the Nekrasov partition function evaluating the equivariant volume of the instanton moduli space. For finite radius we obtain a tower of world-sheet instanton corrections, that we identify with the equivariant Gromov-Witten invariants of the ADHM moduli space. We show that these corrections can be encoded in a deformation of the Seiberg-Witten prepotential. From the mathematical viewpoint, the D1-D5 system under study displays a twofold nature: the D1-branes viewpoint captures the equivariant quantum cohomology of the ADHM instanton moduli space in the Givental formalism, and the D5-branes viewpoint is related to higher rank equivariant Donaldson-Thomas invariants of \( {{\mathbb{P}}^1}\times {{\mathbb{C}}^2} \).
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Bonelli, G., Sciarappa, A., Tanzini, A. et al. The stringy instanton partition function. J. High Energ. Phys. 2014, 38 (2014). https://doi.org/10.1007/JHEP01(2014)038
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DOI: https://doi.org/10.1007/JHEP01(2014)038